Research Article
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Year 2020, Volume 28, Issue 28, 193 - 205, 14.07.2020
https://doi.org/10.24330/ieja.768259

Abstract

References

  • G. Calugareanu, UU rings, Carpathian J. Math., 31(2) (2015), 157-163.
  • M. Chadeyras, Essai d'une theorie noetherienne pour les anneaux commutatifs dont la graduation est aussi generale que possible, Bull. Soc. Math. France Suppl. Mem., 22 (1970), 3-143.
  • H. Chen, On strongly J-clean rings, Comm. Algebra, 38(10) (2010), 3790-3804.
  • P. V. Danchev, Rings with Jacobson units, Toyama Math. J., 38 (2016), 61-74.
  • A. J. Diesl, Nil clean rings, J. Algebra, 383 (2013), 197-211.
  • E. Halberstadt, Le radical d'un anneide regulier, C. R. Acad. Sci. Paris Ser. A, 270 (1970), 361-363.
  • E. Halberstadt, Theorie Artinienne Homogene des Anneaux Gradues a Grades Non Commutatifs Reguliers, Ph.D. Thesis, University of Pierre and Marie Currie (Paris VI), Paris, France, 1971.
  • E. Ilic-Georgijevic, On graded $\Omega$-groups, Filomat, 29(10) (2015), 2167-2183.
  • E. Ilic-Georgijevic, On graded Brown-McCoy radicals of graded rings, J. Algebra Appl., 15(8) (2016), 1650143 (13 pp).
  • E. Ilic-Georgijevic, On graded Thierrin radicals of graded rings, Comm. Algebra, 45(9) (2017), 3886-3891.
  • E. Ilic-Georgijevic, On graded special radicals of graded rings, J. Algebra Appl., 17(6) (2018), 1850109 (10 pp).
  • E. Ilic-Georgijevic, On radicals of graded ring constructions, in Rings, Modules and Codes, Contemp. Math., Amer. Math. Soc., Providence, RI, 727 (2019), 167-176.
  • E. Ilic-Georgijevic and S. Sahinkaya, On graded nil clean rings, Comm. Algebra, 46(9) (2018), 4079-4089.
  • A. V. Kelarev, Combinatorial properties and homomorphisms of semigroups, Internat. J. Algebra Comput., 4(3) (1994), 443-450.
  • A. V. Kelarev, On groupoid graded rings, J. Algebra, 178 (1995), 391-399.
  • A. V. Kelarev, Ring Constructions and Applications, Series in Algebra, 9, World Scienti c Publishing Co., Inc., River Edge, NJ, 2002.
  • A. V. Kelarev and A. Plant, Bergman's lemma for graded rings, Comm. Algebra, 23(12) (1995), 4613-4624.
  • K. Koh, On lifting idempotents, Canad. Math. Bull., 17(4) (1974), 607.
  • M. T. Kosan, A. Leroy and J. Matczuk, On UJ-rings, Comm. Algebra, 46(5) (2018), 2297-2303.
  • M. Krasner, Une generalisation de la notion de corps-corpode, Un corpode remarquable de la theorie des corps values, C. R. Acad. Sci. Paris, 219 (1944), 345-347.
  • M. Krasner, Anneaux gradues generaux, Algebra Colloquium (Rennes, 1980), Univ. Rennes, Rennes, (1980), 209-308.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and Y. Zhou, Strong lifting, J. Algebra, 285(2) (2005), 795-818.
  • W. K. Nicholson and Y. Zhou, Clean general rings, J. Algebra, 291(1) (2005), 297-311.

ON GRADED UJ-RINGS

Year 2020, Volume 28, Issue 28, 193 - 205, 14.07.2020
https://doi.org/10.24330/ieja.768259

Abstract

In this paper, graded rings are $S$-graded rings inducing $S,$ that is, rings whose additive groups can be written as a direct sum of a family of their additive subgroups indexed by a nonempty set $S,$ and such that the product of two homogeneous elements is again a homogeneous element. As a generalization of the recently introduced notion of a $UJ$-ring, we define a graded $UJ$-ring. Graded nil clean rings which are graded $UJ$ are described. We also investigate the graded $UJ$-property under some graded ring constructions.

References

  • G. Calugareanu, UU rings, Carpathian J. Math., 31(2) (2015), 157-163.
  • M. Chadeyras, Essai d'une theorie noetherienne pour les anneaux commutatifs dont la graduation est aussi generale que possible, Bull. Soc. Math. France Suppl. Mem., 22 (1970), 3-143.
  • H. Chen, On strongly J-clean rings, Comm. Algebra, 38(10) (2010), 3790-3804.
  • P. V. Danchev, Rings with Jacobson units, Toyama Math. J., 38 (2016), 61-74.
  • A. J. Diesl, Nil clean rings, J. Algebra, 383 (2013), 197-211.
  • E. Halberstadt, Le radical d'un anneide regulier, C. R. Acad. Sci. Paris Ser. A, 270 (1970), 361-363.
  • E. Halberstadt, Theorie Artinienne Homogene des Anneaux Gradues a Grades Non Commutatifs Reguliers, Ph.D. Thesis, University of Pierre and Marie Currie (Paris VI), Paris, France, 1971.
  • E. Ilic-Georgijevic, On graded $\Omega$-groups, Filomat, 29(10) (2015), 2167-2183.
  • E. Ilic-Georgijevic, On graded Brown-McCoy radicals of graded rings, J. Algebra Appl., 15(8) (2016), 1650143 (13 pp).
  • E. Ilic-Georgijevic, On graded Thierrin radicals of graded rings, Comm. Algebra, 45(9) (2017), 3886-3891.
  • E. Ilic-Georgijevic, On graded special radicals of graded rings, J. Algebra Appl., 17(6) (2018), 1850109 (10 pp).
  • E. Ilic-Georgijevic, On radicals of graded ring constructions, in Rings, Modules and Codes, Contemp. Math., Amer. Math. Soc., Providence, RI, 727 (2019), 167-176.
  • E. Ilic-Georgijevic and S. Sahinkaya, On graded nil clean rings, Comm. Algebra, 46(9) (2018), 4079-4089.
  • A. V. Kelarev, Combinatorial properties and homomorphisms of semigroups, Internat. J. Algebra Comput., 4(3) (1994), 443-450.
  • A. V. Kelarev, On groupoid graded rings, J. Algebra, 178 (1995), 391-399.
  • A. V. Kelarev, Ring Constructions and Applications, Series in Algebra, 9, World Scienti c Publishing Co., Inc., River Edge, NJ, 2002.
  • A. V. Kelarev and A. Plant, Bergman's lemma for graded rings, Comm. Algebra, 23(12) (1995), 4613-4624.
  • K. Koh, On lifting idempotents, Canad. Math. Bull., 17(4) (1974), 607.
  • M. T. Kosan, A. Leroy and J. Matczuk, On UJ-rings, Comm. Algebra, 46(5) (2018), 2297-2303.
  • M. Krasner, Une generalisation de la notion de corps-corpode, Un corpode remarquable de la theorie des corps values, C. R. Acad. Sci. Paris, 219 (1944), 345-347.
  • M. Krasner, Anneaux gradues generaux, Algebra Colloquium (Rennes, 1980), Univ. Rennes, Rennes, (1980), 209-308.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and Y. Zhou, Strong lifting, J. Algebra, 285(2) (2005), 795-818.
  • W. K. Nicholson and Y. Zhou, Clean general rings, J. Algebra, 291(1) (2005), 297-311.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Emil ILIC-GEORGIJEVIC This is me (Primary Author)
University of Sarajevo
Bosnia and Herzegovina

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768259, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {193 - 205}, doi = {10.24330/ieja.768259}, title = {ON GRADED UJ-RINGS}, key = {cite}, author = {Ilıc-georgıjevıc, Emil} }
APA Ilıc-georgıjevıc, E. (2020). ON GRADED UJ-RINGS . International Electronic Journal of Algebra , 28 (28) , 193-205 . DOI: 10.24330/ieja.768259
MLA Ilıc-georgıjevıc, E. "ON GRADED UJ-RINGS" . International Electronic Journal of Algebra 28 (2020 ): 193-205 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768259>
Chicago Ilıc-georgıjevıc, E. "ON GRADED UJ-RINGS". International Electronic Journal of Algebra 28 (2020 ): 193-205
RIS TY - JOUR T1 - ON GRADED UJ-RINGS AU - EmilIlıc-georgıjevıc Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768259 DO - 10.24330/ieja.768259 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 193 EP - 205 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768259 UR - https://doi.org/10.24330/ieja.768259 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra ON GRADED UJ-RINGS %A Emil Ilıc-georgıjevıc %T ON GRADED UJ-RINGS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768259 %U 10.24330/ieja.768259
ISNAD Ilıc-georgıjevıc, Emil . "ON GRADED UJ-RINGS". International Electronic Journal of Algebra 28 / 28 (July 2020): 193-205 . https://doi.org/10.24330/ieja.768259
AMA Ilıc-georgıjevıc E. ON GRADED UJ-RINGS. IEJA. 2020; 28(28): 193-205.
Vancouver Ilıc-georgıjevıc E. ON GRADED UJ-RINGS. International Electronic Journal of Algebra. 2020; 28(28): 193-205.
IEEE E. Ilıc-georgıjevıc , "ON GRADED UJ-RINGS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 193-205, Jul. 2020, doi:10.24330/ieja.768259